Calculation of Thermal Expansion in Insulating and Ceramic Materials

Abstract

A method of calculating thermal expansion in insulating and ceramic materials is presented which makes use of a theory of thermal expansion in terms of the quantum mechanical solutions of the Morse potential. In this model, the localized interatomic potential solutions, obtained from the appropriate Morse potential, are combined with the Debye model to give a localizedcontinuum description of thermal expansion. A set of empirical rules is developed for characterizing the interatomic potential in terms of the parameters of the Morse potential. These are then applied to the quantitative calculation of thermal expansion in the alkali halide crystals and a group of binary high temperature materials with the aid of the known crystal structures, compressibilities, and Debye temperatures of these materials. Good agreement between theoretical and experimental values is obtained for these materials at temperatures ranging from 0°K to values near their melting points. Using further empirical treatment, thermal expansion in a larger group of binary and complex ternary materials is calculated using no experimental input other than the chemical formula. The agreement with experiment is again generally good, though less accurate than when experimental input is used. The results indicate that this approach is capable of predicting the thermal expansion of a wide range of materials with little or no experimental input and no adjustable parameters. The limitations of this method for certain special cases is also discussed.